Billy\'s Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturi

Question

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time, 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time, 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time, 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3,750 labor hours, and he has a budget of $3,000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25. Formulate the LP that maximizes weekly profit.

Explanation / Answer

Let x= number of Astra T-Shirt produced
       y= number of Bling T-Shirt produced
       z= number of Curious T-Shirt produced
Since the objective is to maximize the profit, thus the function
Maximize A= 5x + 4y + 7z ( based on the profit earning by selling each T-Shirt, see column profit above)
subject to some of the constraints

150x + 120y+ 100z <= 300    (Maximum hours machine available- 300 divided by 2, 2.5 & 3 to get 150,120 & 100 ) 187.5x + 125y + 83z <= 3750 ( Maximum hours labor available - 3750 divided by 20,30,& 45 to get values)
300x + 214y + 166z <= 3000 ( Maximum Budget Available - 3000 divided by 10,14 &18 to get values )

x , y , z >= 0    ( for non-negativity constraint)

T-Shirts Machine Time Labour minutes Cost (In $) Selling Price(in $) Profit(in $) Astro 2 20 10 15 5 Bling 2.5 30 14 18 4 Curious 3 45 18 25 7

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.